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This making or imagining of models (not necessarily or usually a material model, but a conceptual model) is a recognised way of arriving at an understanding of recondite and ultra-sensual processes, occurring say in the ether or elsewhere.

Mere deductive logic, whether you clothe it in mathematical symbols and phraseology or whether you enlarge its scope into a more general symbolic technique, can never take the place of clear relevant initial concepts of the meaning of your symbols, and among symbols I include words. If you are dealing with nature, your meanings must directly relate to the immediate facts of observation. We have to analyse first the most general characteristics of things observed, and then the more casual contingent occurrences. There can be no true physical science which looks first to mathematics for the provision of a conceptual model. Such a procedure is to repeat the errors of the logicians of the middle-ages.

The 'physical' does not mean any particular kind of reality, but a particular kind of denoting reality, namely a system of concepts in the natural sciences which is necessary for the cognition of reality. 'The physical' should not be interpreted wrongly as an attribute of one part of reality, but not of the other ; it is rather a word denoting a kind of conceptual construction, as, e.g., the markers 'geographical' or 'mathematical', which denote not any distinct properties of real things, but always merely a manner of presenting them by means of ideas..

The rule is derived inductively from experience, therefore does not have any inner necessity, is always valid only for special cases and can anytime be refuted by opposite facts. On the contrary, the law is a logical relation between conceptual constructions; it is therefore deductible from upper [übergeordnete] laws and enables the derivation of lower laws; it has as such a logical necessity in concordance with its upper premises; it is not a mere statement of probability, but has a compelling, apodictic logical value once its premises are accepted

In the new pattern of thought we do not assume any longer the detached observer, occurring in the idealizations of this classical type of theory, but an observer who by his indeterminable effects creates a new situation, theoretically described as a new state of the observed system. In this way every observation is a singling out of a particular factual result, here and now, from the theoretical possibilities, therefore making obvious the discontinuous aspect of physical phenomena.
Nevertheless, there remains still in the new kind of theory an objective reality, inasmuch as these theories deny any possibility for the observer to influence the result of a measurement, once the experimental arrangement is chosen. Therefore particular qualities of an individual observer do not enter into the conceptual framework of the theory.

Wolfgang Pauli "Matter" in Man's Right to Knowledge, 2nd series (1954), p. 10;

Scientists whose work has no clear, practical implications would want to make their decisions considering such things as: the relative worth of (1) more observations, (2) greater scope of his conceptual model, (3) simplicity, (4) precision of language, (5) accuracy of the probability assignment.

The term architecture is used here to describe the attributes of a system as seen by the programmer, i.e., the conceptual structure and functional behavior, as distinct from the organization of the data flow and controls, the logical design, and the physical implementation. i. Additional details concerning the architecture,

We realize, however, that all scientific laws merely represent abstractions and idealizations expressing certain aspects of reality. Every science means a schematized picture of reality, in the sense that a certain conceptual construct is unequivocally related to certain features of order in reality;

The programmer, like the poet, works only slightly removed from pure thought-stuff. He builds his castles in the air, from air, creating by exertion of the imagination. Few media of creation are so flexible, so easy to polish and rework, so readily capable of realizing grand conceptual structures....
Yet the program construct, unlike the poet's words, is real in the sense that it moves and works, producing visible outputs separate from the construct itself. […] The magic of myth and legend has come true in our time. One types the correct incantation on a keyboard, and a display screen comes to life, showing things that never were nor could be.

Ludwig von Bertalanffy, a distinguished biologist, occupies an important position in the intellectual history of the twentieth century. His contributions went beyond biology, and extended to psychology, psychiatry, sociology, cybernetics, history and philosophy. Some of his admirers even believe that von Bertalanffy's general systems theory could provide a conceptual framework for all these disciplines.

I strongly reject any conceptual scheme that places our options on a line, and holds that the only alternative to a pair of extreme positions lies somewhere between them. More fruitful perspectives often require that we step off the line to a site outside the dichotomy.

A conceptual model is a qualitative description of the system and includes the processes taking place in the system, the parameters chosen to describe the processes, and the spatial and temporal scales of the processes.

A conceptual model is a representation of the system expertise using this formalism. An internal model is derived from the conceptual model and from a specification of the system transactions and the performance constraints.

Truly grand and powerful theories […] do not and cannot rest upon single observations. Evolution is an inference from thousands of independent sources, the only conceptual structure that can make unified sense of all this disparate information. The failure of a particular claim usually records a local error, not the bankruptcy of a central theory. […] If I mistakenly identify your father's brother as your own dad, you don't become genealogically rootless and created de novo. You still have a father; we just haven't located him properly.

When we entrust the domain of values to those whose intellectual concerns are essentially centred on empirical facts, and whose conceptual frameworks are inevitably constructed around sets of empirical facts, we need not be surprised if the result is moral confusion.

The purpose of a conceptual model is to provide a vocabulary of terms and concepts that can be used to describe problems and/or solutions of design. It is not the purpose of a model to address specific problems, and even less to propose solutions for them. Drawing an analogy with linguistics, a conceptual model is analogous to a language, while design patterns are analogous to rhetorical figures, which are predefined templates of language usages, suited particularly to specific problems.

Sometimes, however, a conceptual model is only a first step, and the second step is a mathematical representation of the conceptual model

Gregory N. Derry (2002) What Science Is and How It Works. p. 71.

What surprised me, which Google was part of, is that superficial search techniques over large bodies of stuff could get you what you wanted. I grew up in the AI tradition, where you have a complete conceptual model, and the information retrieval tradition, where you have complex vectors of key terms and Boolean queries. The idea that you can index billions of pages and look for a word and get what you want is quite a trick. To put it in more abstract terms, it's the power of using simple techniques over very large numbers versus doing carefully constructed systematic analysis.

A conceptual level view of an object design describes the key abstractions. While someone might think of key abstractions as being nothing more or nothing less than high-level descriptions of "candidate classes", I prefer to consider a conceptual design from a slightly different angle--I'm thinking about design at a slightly different level.
An object-oriented application is a set of interacting objects. Each object is an implementation of one or more roles. A role supports a set of related (cohesive) responsibilities. A responsibility is an obligation to perform a task or know certain information. And objects don't work in isolation, they collaborate with others in a community to perform the overall responsibilities of the application. So a conceptual view, at least to start, is a distillation of the key object roles and their responsibilities (stated at a fairly high level). More than likely (unless you form classification hierarchies and use inheritance and composition techniques) many candidates you initially model will map directly to a single class in some inheritance hierarchy. But I like to open up possibilities by think first of roles and responsibilities, and then as a second step towards a specification-level view, mapping these candidates to classes and interfaces.

The conceptual model is a non-software specific description of the simulation model that is to be developed, describing the objectives, inputs, outputs, content, assumptions and simplifications of the model.

Stewart Robinson (2004) Simulation: The Practice of Model Development and Use. p. 65.

A conceptual model is a mental image of a system, its components, its interactions. It lays the foundation for more elaborate models, such as physical or numerical models. A conceptual model provides a framework in which to think about the workings of a system or about problem solving in general. An ensuing operational model can be no better than its underlying conceptualization.

H. N. Pollack (2005) Uncertain Science … Uncertain World. p. 107.

Within sociology there have been several system theories, differing from one another in the extent to which, for example, human agency, creativity, and entrepreneurship are assumed to play a role in system formation and reformation; conflict and struggle are taken into account; power and stratification are part and parcel of the theory; structural change and transformation – and more generally, historically developments – are taken into account and explained. What the various system theories have in common is a systematic concern with complex and varied interconnections and interdependencies of social life. Complexity has been a central concept for many working in the systems perspective. The tradition is characterized to a great extent by a burning ambition and hope to provide a unifying language and conceptual framework for all the social sciences.

Tom R. Burns (2006) Systems theories p. 1.

The role of conceptual modelling in information systems development during all these decades is seen as an approach for capturing fuzzy, ill-defined, informal "real-world" descriptions and user requirements, and then transforming them to formal, in some sense complete, and consistent conceptual specifications.

The first function of a conceptual model is relating the research to the existing body of literature. With the help of a conceptual model a researcher can indicate in what way he is looking at the phenomenon of his research.

Conceptual models are best thought of as design-tools — a way for designers to straighten out and simplify the design and match it to the users' task-domain, thereby making it clearer to users how they should think about the application.